Post on 19-Aug-2018
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
NanoBio Spectroscopy Group, Dpto. Física de Materiales, Universidad del País Vasco,
Centro Mixto CSICUPV/EHU and DIPC Edificio Korta, San Sebastián, Spain
http://nanobio.ehu.es Email: angel.rubio@.ehu.es
Angel Rubio
Spectroscopy of nanostructures: from optics to transport
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
OUTLINE
Introduction: Framing the lecture: spectroscopiesExcitations; response concepts
Application to finite systems:Linear Response applications : “small clusters, phenolates and porphyrines”
Photovoltaic applications: simple hybrid system
Electronic transport Concepts in molecular transport
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Physical Processes: Spectroscopies
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Physical Processes: Spectroscopies
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Time-dependent phenomena!
Photoexcitation and relaxation
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
See review: G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)
Electronic properties of a many body system
Ground state
density n(r)yes, LDA, GGA's
n(r,t) and/or j(r,t)
G1, total energy
G2
yes
Excited states
Corrections toKS eigenvalues?
Yes, non-linear phenomena and
time-resolved spectroscopies
Quasiparticle excitationsIP and EA
optical absorption
yes, in some cases!
Scheme
DFT
TDDFT
MBPT
QM
Disadvantages
XC-func.
(r,r') (w)dependence
Comput.
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Density Functional versus Manybody perturbation theory
groundstate
What about excited-state properties: electron-ion dynamics, spectroscopies
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Can we calculate spectra with DFT?
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
What is a spectrum?
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Vinduced
= n v + fxc
n
Hartree
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Beyond DFT
Bethe-Salpeter eqn:
Im [] ~ vc
|<v|D|c>|2 (Ec-E
v-)
Im [] ~ s |
vc<v|D|c>A
vcS|2 (S)
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Time Dependent Density Functional Theory (Runge and Gross 1984):
All observables are functionals of the TD density
?
One-to-one correspondence between the time-dependent density and the external potential, v(r,t) <------> (r,t)
Time-Dependent Density Functional Theory, Lecture Notes in Physics, Vol. 706 (Springer, Berlin, 2006)
Same time-dependent
density n(r,t)
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Time Dependent Density Functional Theory (Runge and Gross 1984):
All observables are functionals of the TD density
i ℏddt
=H i ℏddti=H KS [ { j } ]i , i=1,⋯N ?
H KS=ℏ
2
2mi∇−
ecℏ
AAxc2
V externalV hartreeV exchangeV correlation
One-to-one correspondence between the time-dependent density and the external potential, v(r,t) <------> (r,t)
Time-Dependent Density Functional Theory, Lecture Notes in Physics, Vol. 706 (Springer, Berlin, 2006)
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
TDDFT does the job for you!!!
Vext
however the KS system Veff
=00v f xc
0 r ,r ' ,w=∑ij f j− f i
icr jr i r ' j
cr '
i− j−wf xcr , r ' ,=
V xcr ,
n r ,
Linear Response
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
How to solve the linear response equations
(1) Sum over states: 0 r ,r ' , w=∑ij f j− f i
icr jr i r ' j
cr '
i− j−w
=00v f xc
Cassida's approach
[1−v f xc0]=0
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
How to solve the linear response equations
(2) Time propagation
Propagation Scheme:●Apply a perturbation of the form vext (r,t) = −z(t) to the ground state of the system●At t = 0+ the Kohn-Sham orbitals are
(r,t=0+)= eikz
(r )
●Propagate these KS wave-functions for a (in)finite time.●The dynamical polarizability can be obtained from k-1
z
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
How to solve the linear response equations
(3) Density Functional Perturbation Theory
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Optical Spectroscopy
optical gap transport gap photoemision (QP) gap
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Optical response:
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Steen Bronsted Nielsen et al, ChemPhysChem (2009)
Absorption Spectra of pNitrophenolate Ions in Vacuo and in Solution
serve as donoracceptor molecules
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Absorption Spectra of pNitrophenolate Ions in Vacuo and in Solution
Steen Bronsted Nielsen et al, ChemPhysChem (in press 2009)
300 400 500 600 700 800 900 1000
W avelength / nm
1
2
3
Ab
so
rpti
on
/ a
rb.
un
its
4
Fluctuations due to planar-non planar geometries ~0.1-0.2 eV(2 and 4 are not planar in DFT)
CT is slightly favor by torsion of phenyl rings
HOMO LUMO
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Absorption Spectra of pNitrophenolate Ions in Vacuo and in Solution
O NO2
hS0
S1
O NO2
O NO2
From blue to red: in vacuo they cover the full visible whereas in solution they absorb in a narrow energy region
The solvent shift is mainly due to counter ion and H-bond interactions, then the results do not correlate with solvent polarity
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Towards the color of plants:
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Towards the color of plants: The real Chlorophyll molecule
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Towards the color of plants: The real Chlorophyll molecule
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Towards the color of plants: The real Chlorophyll molecule
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Photovoltaics Hybrids
Grätzel cells
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
CT: Photo-excitation of the light-harvesting carotenoid-porphyrin-C60
N. Spallanzine et al, J. Phys. Chem. B, 2009, 113 (2009)
?
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Photo-excitation of the light-harvesting carotenoid-porphyrin-C60
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Clamped ions
Charge on the C60
Dynamical ionsClamped ions
Carotenoid-porphyrin-C60 photodynamics
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
35
Quantum Transport
Ab-initio model
Non-equilibrium
Quantum Mechanics
Many-body problem
I(t)=I([U]); Conductance G=I/U for steady state
Thanks to R. Godby
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Applying a bias voltage
The bias can affect the HOMO-LUMO gap
The bias can affect the resonance width
These effects must be taken into account to describe the IV
Molecular DOS
Current: (Landauer)!
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
37
Experiments & modelling
X. D. Cui et al. Science, Vol 294, 571-574 (2001)
Experiments:
Octanedithiol/Au: R ≈ 900 MΩ [X. D. Cui et al., Science (2001).]Benzene-di-amin/Au: R ≈ 2 MΩ [Quek, Nano Lett. (2007).]Benzene-di-thiol/Au: R ≈ 18±12 MΩ [M. A. Reed et al. Science (1997).]H2/Pt: G ≈ 0.95 G0 (≈ 1/(13 kΩ))
1
[R.H.M.Smit et al. Nature (2002).]
Theory – Density Functional Theory + NEGF:
for G ≈ G0 generally goodfor G << G0 poor e.g. G ≈ 0.046 G0 for Benzene-di-amin/Au [Quek, Nano Lett. (2007).]
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
LEVEL ALIGNMENT, Dispersion forces VdW
Aromatic molecules on
Cu(110)
N. Atodiresei, S.Blugel et al, PRL 102, 136809 (2009)
See the talk of P. Rinke for CO on surfaces
Supramolecular chemistry
Biophysics ..........
Molecular Transport
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
MOLECULAR TRANSPORT : LEVEL ALIGNMENT
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Molecular Transport in TDDFT
G. Stefanucci, S. Kurth, AR and E.K.U Gross "Molecular electronics: analysis, design, and simulation", J. Seminario, ed(s), Elsevier Series on Theoretical and Computational Chemistry (2007); PRB (2005)
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Example: Electron pumping
G. Stefanuci, S. Kurth, AR and E.K.U. Gross; PRB (2008)
Device which generates a net current between two electrodes (with NO static bias) by applying a time-dependent potential in the device region
Recent experimental realization : Pumping through carbon nanotube by surface acoustic waves on piezoelectric surface (Leek et al, PRL 95, 256802 (2005))
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Example: Electron pumping
net current in the device by applying a TD potential to the device regionRealisation: pumping in C nanotubes using surface acustic waves (Archimidean screw, ca. 250 bc)
G. Stefanuci, S. Kurth, AR and E.K.U. Gross; PRB (2007)
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
OUTLOOK/PERSPECTIVETDDFT is a powerful tool to handle the combined dynamics of electron/ion in
response to external electromagnetic fields of nanostructures, biological molecules and extended systems.
● Ehrenfest dynamics provides valuable insight but with limitations● Speed-up using a new Lagrangian formulation similar to CP● The optics of low-dimensional structures is dominated by excitons● Environment and T effects are important
Work to be done:Memory effects l Dissipation ; lifetimes ; de-coherence
Spatial non-locality: Charge-transfer excitations; Non-adiabatic effects in excite state ion dynamics (related to geometrical phases)
Spectroscopy of nanostructures: from optics to transport XI Escuela Nacional de Materiales Moleculares, Peñafiel 1419 Feb 2010
Workshop “Non adiabati
c dynamic
s at surfaces
”, Schloss Reisens
burg October
2007
12th Density Functional Theory Conference, Amsterdam, August 2007
Than
k yo
u!!!!
For more details see:http://nano-bio.ehu.eshttp://etsf.eu